Why does a real image form on the other side of a convex lens but a virtual image doesn't?

An image is real when the refracted (or reflected) rays actually meet at a point after passing through the lens, and you can catch a real image on a screen. With a convex lens, this happens when the object is beyond the focus; the rays converge on the opposite side and form an inverted, real image. An image is virtual when the rays do not actually meet but only appear to come from a point when extended backward. You cannot catch a virtual image on a screen. With a convex lens this happens when the object is between the lens and its focus, giving an upright, magnified virtual image on the same side as the object, like a magnifying glass. So check whether the actual rays converge or only their backward extensions do.